A new notion of rank for finite supersolvable groups and free linear actions on products of spheres
| dc.citation.epage | 364 | en_US |
| dc.citation.issueNumber | 3 | en_US |
| dc.citation.spage | 347 | en_US |
| dc.citation.volumeNumber | 6 | en_US |
| dc.contributor.author | Barker, L. | en_US |
| dc.contributor.author | Yalçın, E. | en_US |
| dc.date.accessioned | 2016-02-08T10:30:48Z | |
| dc.date.available | 2016-02-08T10:30:48Z | |
| dc.date.issued | 2003 | en_US |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | For a finite supersolvable group G, we define the saw rank of G to be the minimum number of sections Gk/Gk-1 of a cyclic normal series G* such that Gk -Gk-1 contains an element of prime order. The axe rank of G, studied by Ray [10], is the minimum number of spheres in a product of spheres admitting a free linear action of G. Extending a question of Ray, we conjecture that the two ranks are equal. We prove the conjecture in some special cases, including that where the axe rank is 1 or 2. We also discuss some relations between our conjecture and some questions about Bieberbach groups and free actions on tori. | en_US |
| dc.identifier.issn | 1433-5883 | |
| dc.identifier.uri | http://hdl.handle.net/11693/24538 | |
| dc.language.iso | English | en_US |
| dc.publisher | Walter de Gruyter GmbH | en_US |
| dc.source.title | Journal of Group Theory | en_US |
| dc.title | A new notion of rank for finite supersolvable groups and free linear actions on products of spheres | en_US |
| dc.type | Article | en_US |
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